The generator matrix

 1  1  1  1  1  1 X^3  1  1  1 X^2  X  1
 0  X  0  X  0 X^3 X^2 X^3+X X^2+X  0 X^2  X  0
 0  0  X  X X^3+X^2 X^3+X^2+X  X X^2+X  0 X^2+X  X  X  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3
 0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3

generates a code of length 13 over Z2[X]/(X^4) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+34x^9+154x^10+258x^11+933x^12+1342x^13+933x^14+252x^15+153x^16+30x^17+2x^19+1x^20+2x^21+1x^22

The gray image is a linear code over GF(2) with n=104, k=12 and d=36.
This code was found by Heurico 1.16 in 0.032 seconds.